```python
"""The cheapest set of travel passes covering every trip day."""


def _validate_plan(trip_days, passes):
    for day in trip_days:
        if isinstance(day, bool) or not isinstance(day, int) or day < 1:
            raise ValueError("trip days must be positive integers")
    for earlier, later in zip(trip_days, trip_days[1:]):
        if later <= earlier:
            raise ValueError("trip days must be strictly increasing")
    if not passes:
        raise ValueError("at least one pass kind is required")
    for cover in passes:
        span = cover["span"]
        cost = cover["cost"]
        if isinstance(span, bool) or not isinstance(span, int) or span < 1:
            raise ValueError("pass span must be a positive integer")
        if isinstance(cost, bool) or not isinstance(cost, int) or cost < 0:
            raise ValueError("pass cost must be a non-negative integer")


def cheapest_pass_plan(trip_days: list, passes: list) -> dict:
    _validate_plan(trip_days, passes)
    if not trip_days:
        return {"total": 0, "purchases": []}
    
    trip_days = sorted(trip_days)
    cheapest_purchases = []
    total_cost = 0
    
    for day in trip_days:
        for cover in passes:
            if day >= cover["start"] and day <= cover["start"] + cover["span"] - 1:
                cheapest_purchases.append([cover["start"], cover["span"]])
                total_cost += cover["cost"]
                break
    
    return {"total": total_cost, "purchases": cheapest_purchases}
```